How to force inter bank lending rates down. (UK)

We have a situation where base rates are far below inter bank lending rates. The British government has part nationalised and totally guaranteed our own banks. The banks that it has guaranteed can be forced to lend to each other.

My question:

1. Does this keep those banks safe?
2. Does it break international trade rules and so lead to a protectionist depression? (Remember it's only the banks that it's guaranteeing, but it has to ensure they don't get aggressive on trade in this temporary state, methinks).